The signum (or sign) function, denoted by sgn, is defined by

Question

The signum (or sign) function, denoted by sgn, is defined by

sgn x =	−1	if	x < 0
0	if	x = 0
1	if	x > 0

.

(a) Sketch the graph of this function.

(b) Find each of the following limits. (If an answer does not exist, enter DNE.)

(i) lim x→0⁺ sgn x

(ii) lim x→0⁻ sgn x

(iii) lim x→0 sgn x

(iv) lim x→0 |sgn x|

Answer 1